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Generalization of the golden ratio (expansion of (5-13x)/((1+x)(1-4x))).
(Formerly M3735)
1

%I M3735 #22 Dec 20 2017 23:28:26

%S 5,2,26,86,362,1430,5738,22934,91754,366998,1468010,5872022,23488106,

%T 93952406,375809642,1503238550,6012954218,24051816854,96207267434,

%U 384829069718,1539316278890,6157265115542,24629060462186

%N Generalization of the golden ratio (expansion of (5-13x)/((1+x)(1-4x))).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D A. K. Whitford, A generalization of the golden ratio, J. Rec. Math., 8 (No. 3, 1975-1976), 203-207.

%H A. K. Whitford, <a href="/A007572/a007572.pdf">A generalization of the golden ratio</a>, J. Rec. Math., 8 (No. 3, 1975-1976), 203-207. (Annotated scanned copy)

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3, 4).

%F a(0)=5, a(1)=2, a(n)=3*a(n-1)+4*a(n-2). [_Harvey P. Dale_, Apr 15 2012]

%t CoefficientList[Series[(5-13x)/((1+x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{3,4},{5,2},30] (* _Harvey P. Dale_, Apr 15 2012 *)

%K nonn

%O 0,1

%A _Simon Plouffe_ and _N. J. A. Sloane_, _Robert G. Wilson v_

%E Clarified definition by _Harvey P. Dale_, Apr 15 2012